Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics
Joint Authors
Lee, Sunhong
Kim, Gwang-Il
Lee, Hyun Chol
Lee, Mi Ran
Jeong, Seungpil
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-04-23
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
We present an algorithm for C1 Hermite interpolation using Möbius transformations of planar polynomial Pythagoreanhodograph (PH) cubics.
In general, with PH cubics, we cannot solve C1 Hermite interpolation problems, since their lack of parameters makes the problems overdetermined.
In this paper, we show that, for each Möbius transformation, we can introduce an extra parameter determined by the transformation, with which we can reduce them to the problems determining PH cubics in the complex plane ℂ.
Möbius transformations preserve the PH property of PH curves and are biholomorphic.
Thus the interpolants obtained by this algorithm are also PH and preserve the topology of PH cubics.
We present a condition to be met by a Hermite dataset, in order for the corresponding interpolant to be simple or to be a loop.
We demonstrate the improved stability of these new interpolants compared with PH quintics.
American Psychological Association (APA)
Lee, Sunhong& Lee, Hyun Chol& Lee, Mi Ran& Jeong, Seungpil& Kim, Gwang-Il. 2012. Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-480746
Modern Language Association (MLA)
Lee, Sunhong…[et al.]. Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics. Abstract and Applied Analysis No. 2012 (2012), pp.1-15.
https://search.emarefa.net/detail/BIM-480746
American Medical Association (AMA)
Lee, Sunhong& Lee, Hyun Chol& Lee, Mi Ran& Jeong, Seungpil& Kim, Gwang-Il. Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-480746
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-480746